The transplantation of allogeneic peripheral blood progenitor cells (PBPC) provides complete and sustained hematopoietic and lymphopoietic engraftment. In healthy donors, large amounts of PBPC can be mobilized with hematopoietic growth factors. However, the high content of immunocompetent T-cells in apheresis products may expose recipients of allogeneic PBPC to an elevated risk of acute and chronic graft-versus-host disease. Thus, the use of appropriate T-cell reduction, but not depletion might reduce this risk. The hazards of graft rejection and a higher relapse rate can be avoided by maintaining a portion of the T-cells in the graft. The positive selection of CD34+ cells from peripheral blood preparations simultaneously provides an approximately 1000-fold reduction of T-cells. These purified CD34+ cells containing committed and pluripotent stem cells are suitable for allogeneic transplantation and can be used in the following instances: 1. As hematopoietic stem and progenitor cell transplantation instead of bone marrow cells, from HLA-identical family donors; 2. for increasing the stem cell numbers from HLA-mismatched or three HLA-loci different family donors in order to reduce the incidence of rejection but without increasing the T-cell number; 3. boosting of poor marrow graft function with stem cells from the same family donors; 4. transplantation from volunteer matched unrelated donors; 5. split transplantation of CD34+ and T-cells; 6. addition of ex vivo expanded CD34+ cells to blood cell or bone marrow transplantation; 7. generation of antigen specific immune effector cells and antigen presenting cells for cell therapy.